Physical Review Letters

Dynamic Measurement of Percolative Critical Exponents in Disordered Josephson Junction Arrays

Ali L. Eichenberger, J. Affolter, M. Willemin, M. Mombelli, H. Beck, Piero Martinoli, S. E. Korshunov

Published Oct 28, 1996• 19 citations

Abstract

The complex conductance $G(\ensuremath{\omega})$ of site-diluted Josephson junction arrays close to the percolation threshold was measured over a wide range of frequencies \ensuremath{\omega}. Well below ${T}_{c}$ both the superfluid $[\ensuremath{\omega}\mathrm{Im}G]$ and dissipative $[\mathrm{Re}G]$ components are independent of \ensuremath{\omega} below a critical frequency ${\ensuremath{\omega}}_{c}$, whereas $G(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\omega}}^{\ensuremath{-}u}$ with $u\ensuremath{\approx}\frac{1}{2}$ for $\ensuremath{\omega}>{\ensuremath{\omega}}_{c}$. This is shown to reflect the crossover from a Euclidean regime $(\ensuremath{\omega}<{\ensuremath{\omega}}_{c})$ dominated by phononlike modes of the phase system to a fractal regime $(\ensuremath{\omega}>{\ensuremath{\omega}}_{c})$, where the relevant excitations are localized fractons. Percolative critical exponents extracted from the data are consistent with theoretical predictions.

DOI: 10.1103/physrevlett.77.3905

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Phase Transition and Critical Dynamics in Site-Diluted Josephson-Junction Arrays

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Current-voltage characteristics of diluted Josephson-junction arrays: Scaling behavior at current and percolation threshold

Enzo Granato, Daniel Domı́nguez

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Sep 14, 20101 citation

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Physical Review Letters

Dynamic Measurement of Percolative Critical Exponents in Disordered Josephson Junction Arrays

Ali L. Eichenberger, J. Affolter, M. Willemin, M. Mombelli, H. Beck, Piero Martinoli, S. E. Korshunov

Published Oct 28, 1996• 19 citations

Publisher

Abstract

The complex conductance

G(\ensuremath{\omega})

of site-diluted Josephson junction arrays close to the percolation threshold was measured over a wide range of frequencies \ensuremath{\omega}. Well below

{T}_{c}

both the superfluid

[\ensuremath{\omega}\mathrm{Im}G]

and dissipative

[\mathrm{Re}G]

components are independent of \ensuremath{\omega} below a critical frequency

{\ensuremath{\omega}}_{c}

, whereas

G(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\omega}}^{\ensuremath{-}u}

with

u\ensuremath{\approx}\frac{1}{2}

for

\ensuremath{\omega}>{\ensuremath{\omega}}_{c}

. This is shown to reflect the crossover from a Euclidean regime

(\ensuremath{\omega}<{\ensuremath{\omega}}_{c})

dominated by phononlike modes of the phase system to a fractal regime

(\ensuremath{\omega}>{\ensuremath{\omega}}_{c})

, where the relevant excitations are localized fractons. Percolative critical exponents extracted from the data are consistent with theoretical predictions.

DOI: 10.1103/physrevlett.77.3905

Related papers

Phase Transition and Critical Dynamics in Site-Diluted Josephson-Junction Arrays

Young-Je Yun, In-Cheol Baek, Mu-Yong Choi

Measurements of the IV characteristics of site-diluted Josephson-junction arrays have revealed intriguing effects of percolative disorder on the phase transition and the vortex dynamics in a two-dimensional XY system. Different from other types of phase transitions, the Kosterlitz-Thouless transition was eliminated with the introduction of percolative disorder far below the percolation threshold. Even after the Kosterlitz-Thouless order had been removed, the system remained superconducting at low temperatures by establishing a different type of order. Near the percolation threshold, evidence was found that, as a consequence of the underlying fractal structure, the critical dynamics of the phase degrees of freedom persisted down to zero temperature.Measurements of the IV characteristics of site-diluted Josephson-junction arrays have revealed intriguing effects of percolative disorder on the phase transition and the vortex dynamics in a two-dimensional XY system. Different from other types of phase transitions, the Kosterlitz-Thouless transition was eliminated with the introduction of percolative disorder far below the percolation threshold. Even after the Kosterlitz-Thouless order had been removed, the system remained superconducting at low temperatures by establishing a different type of order. Near the percolation threshold, evidence was found that, as a consequence of the underlying fractal structure, the critical dynamics of the phase degrees of freedom persisted down to zero temperature.

arXiv:cond-mat/0610688Physical Review LettersNov 20, 200620 citations

Current-voltage characteristics of diluted Josephson-junction arrays: Scaling behavior at current and percolation threshold

Enzo Granato, Daniel Domı́nguez

Dynamical simulations and scaling arguments are used to study the current-voltage $(I\ensuremath{-}V)$ characteristics of a two-dimensional model of resistively shunted Josephson-junction arrays in presence of percolative disorder, at zero external field. Two different limits of the Josephson-coupling concentration $p$ are considered, where ${p}_{c}$ is the percolation threshold. For $p>{p}_{c}$ and zero temperature, the $I\ensuremath{-}V$ curves show power-law behavior above a disorder-dependent critical current. The power-law behavior and critical exponents are consistent with a simple scaling analysis. At ${p}_{c}$ and finite temperature $T,$ the results show the scaling behavior of a $T=0$ superconducting transition. The resistance is linear but vanishes for decreasing $T$ with an apparent exponential behavior. Crossover to nonlinearity appears at currents proportional to ${T}^{1+{\ensuremath{\nu}}_{T}},$ with a thermal-correlation length exponent ${\ensuremath{\nu}}_{T}$ consistent with the corresponding value for the diluted $\mathrm{XY}$ model at ${p}_{c}.$ Dynamical simulations and scaling arguments are used to study the current-voltage $(I\ensuremath{-}V)$ characteristics of a two-dimensional model of resistively shunted Josephson-junction arrays in presence of percolative disorder, at zero external field. Two different limits of the Josephson-coupling concentration $p$ are considered, where ${p}_{c}$ is the percolation threshold. For $p>{p}_{c}$ and zero temperature, the $I\ensuremath{-}V$ curves show power-law behavior above a disorder-dependent critical current. The power-law behavior and critical exponents are consistent with a simple scaling analysis. At ${p}_{c}$ and finite temperature $T,$ the results show the scaling behavior of a $T=0$ superconducting transition. The resistance is linear but vanishes for decreasing $T$ with an apparent exponential behavior. Crossover to nonlinearity appears at currents proportional to ${T}^{1+{\ensuremath{\nu}}_{T}},$ with a thermal-correlation length exponent ${\ensuremath{\nu}}_{T}$ consistent with the corresponding value for the diluted $\mathrm{XY}$ model at ${p}_{c}.$

arXiv:cond-mat/9709012Physical review. B, Condensed matterDec 1, 199715 citations

Phase transition in site-diluted Josephson junction arrays: A numerical study

Jian-Ping Lv, Huan Liu, Qing‐Hu Chen

We numerically investigate the intriguing effects produced by random percolative disorder in two-dimensional Josephson junction arrays. By dynamic scaling analysis, we evaluate critical temperatures and critical exponents with high accuracy. It is observed that with the introduction of site-diluted disorder, the Kosterlitz-Thouless phase transition is eliminated and evolves into a continuous transition with power-law divergent correlation length. Moreover, genuine depinning transition and creep motion are studied; evidence for distinct creep motion types is provided. Our results not only are in good agreement with the recent experimental findings but also shed some light on the relevant phase transitions.We numerically investigate the intriguing effects produced by random percolative disorder in two-dimensional Josephson junction arrays. By dynamic scaling analysis, we evaluate critical temperatures and critical exponents with high accuracy. It is observed that with the introduction of site-diluted disorder, the Kosterlitz-Thouless phase transition is eliminated and evolves into a continuous transition with power-law divergent correlation length. Moreover, genuine depinning transition and creep motion are studied; evidence for distinct creep motion types is provided. Our results not only are in good agreement with the recent experimental findings but also shed some light on the relevant phase transitions.

arXiv:0805.2428Physical Review BMar 16, 200917 citations

Phase transitions in site-diluted Josephson junction arrays

Jian-Ping Lv, Huan Liu, Qing‐Hu Chen

We numerically investigate the intriguing effects produced by random percolative disorder in two-dimensional Josephson-junction arrays. By dynamic scaling analysis, we evaluate critical temperatures and critical exponents with high accuracy. It is observed that, with the introduction of site-diluted disorder, the Kosterlitz-Thouless phase transition is eliminated and evolves into a continuous transition with power-law divergent correlation length. Moreover, genuine depinning transition and creep motion are studied, evidence for distinct creep motion types is provided. Our results not only are in good agreement with the recent experimental findings, but also shed some light on the relevant phase transitions.We numerically investigate the intriguing effects produced by random percolative disorder in two-dimensional Josephson-junction arrays. By dynamic scaling analysis, we evaluate critical temperatures and critical exponents with high accuracy. It is observed that, with the introduction of site-diluted disorder, the Kosterlitz-Thouless phase transition is eliminated and evolves into a continuous transition with power-law divergent correlation length. Moreover, genuine depinning transition and creep motion are studied, evidence for distinct creep motion types is provided. Our results not only are in good agreement with the recent experimental findings, but also shed some light on the relevant phase transitions.

May 16, 20080 citations

Complex critical exponents in quantum percolation transitions

Rafael M. Fernandes, Jörg Schmalian

We show that the critical behavior of quantum systems undergoing a percolation transition is dramatically affected by their topological Berry phase $2\pi\rho$ . For irrational $\rho$ , we demonstrate that the low-energy excitations of diluted Josephson-junctions arrays, quantum antiferromagnets, and interacting bosons are spinless fermions with fractal spectrum. As a result, critical properties not captured by the usual Ginzburg-Landau-Wilson description of phase transitions emerge, such as complex critical exponents, log-periodic oscillations and dynamically broken scale-invariance.We show that the critical behavior of quantum systems undergoing a percolation transition is dramatically affected by their topological Berry phase $2\pi\rho$. For irrational $\rho$, we demonstrate that the low-energy excitations of diluted Josephson-junctions arrays, quantum antiferromagnets, and interacting bosons are spinless fermions with fractal spectrum. As a result, critical properties not captured by the usual Ginzburg-Landau-Wilson description of phase transitions emerge, such as complex critical exponents, log-periodic oscillations and dynamically broken scale-invariance.

Sep 14, 20101 citation

Dynamic critical behaviors in two-dimensional Josephson junction arrays with positional disorder

Jaegon Um, Beom Jun Kim, Petter Minnhagen +2 more

We numerically investigate dynamic critical behaviors of two-dimensional (2D) Josephson-junction arrays with positional disorder in the scheme of the resistively shunted junction dynamics. Large-scale computation of the current-voltage characteristics reveals evidence supporting that a phase transition occurs at a nonzero critical temperature in the strong disorder regime, as well as in the weak disorder regime. The phase transition at weak disorder appears to belong to the Berezinskii-Kosterlitz-Thouless (BKT) type. In contrast, evidence for a non-BKT transition is found in the strong disorder regime. These results are consistent with the recent experiment on positionally disordered Josephson-junction arrays; in particular, the critical temperature of the non-BKT transition (ranging from 0.265 down to the minimum 0.22 in units of ${E}_{J}∕{k}_{B}$ with the Josephson coupling strength ${E}_{J}$ ), the correlation length critical exponent $\ensuremath{\nu}=1.2$, and the dynamic critical exponent $z=2.0$ in the strong disorder regime agree with the existing studies of the 2D gauge-glass model.We numerically investigate dynamic critical behaviors of two-dimensional (2D) Josephson-junction arrays with positional disorder in the scheme of the resistively shunted junction dynamics. Large-scale computation of the current-voltage characteristics reveals evidence supporting that a phase transition occurs at a nonzero critical temperature in the strong disorder regime, as well as in the weak disorder regime. The phase transition at weak disorder appears to belong to the Berezinskii-Kosterlitz-Thouless (BKT) type. In contrast, evidence for a non-BKT transition is found in the strong disorder regime. These results are consistent with the recent experiment on positionally disordered Josephson-junction arrays; in particular, the critical temperature of the non-BKT transition (ranging from 0.265 down to the minimum 0.22 in units of ${E}_{J}∕{k}_{B}$ with the Josephson coupling strength ${E}_{J}$), the correlation length critical exponent $\ensuremath{\nu}=1.2$, and the dynamic critical exponent $z=2.0$ in the strong disorder regime agree with the existing studies of the 2D gauge-glass model.

arXiv:cond-mat/0608390Physical Review BSep 28, 200610 citations

The complex conductance

G(\ensuremath{\omega})

of site-diluted Josephson junction arrays close to the percolation threshold was measured over a wide range of frequencies \ensuremath{\omega}. Well below

{T}_{c}

both the superfluid

[\ensuremath{\omega}\mathrm{Im}G]

and dissipative

[\mathrm{Re}G]

components are independent of \ensuremath{\omega} below a critical frequency

{\ensuremath{\omega}}_{c}

, whereas

G(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\omega}}^{\ensuremath{-}u}

with

u\ensuremath{\approx}\frac{1}{2}

for

\ensuremath{\omega}>{\ensuremath{\omega}}_{c}

. This is shown to reflect the crossover from a Euclidean regime

(\ensuremath{\omega}<{\ensuremath{\omega}}_{c})

dominated by phononlike modes of the phase system to a fractal regime

(\ensuremath{\omega}>{\ensuremath{\omega}}_{c})

, where the relevant excitations are localized fractons. Percolative critical exponents extracted from the data are consistent with theoretical predictions.

p

are considered, where

{p}_{c}

is the percolation threshold. For

p>{p}_{c}

and zero temperature, the $I\ensuremath{-}V$ curves show power-law behavior above a disorder-dependent critical current. The power-law behavior and critical exponents are consistent with a simple scaling analysis. At

{p}_{c}

and finite temperature

T,

the results show the scaling behavior of a

T=0

superconducting transition. The resistance is linear but vanishes for decreasing

T

with an apparent exponential behavior. Crossover to nonlinearity appears at currents proportional to ${T}^{1+{\ensuremath{\nu}}_{T}},$ with a thermal-correlation length exponent ${\ensuremath{\nu}}_{T}$ consistent with the corresponding value for the diluted

\mathrm{XY}

model at

{p}_{c}.

We show that the critical behavior of quantum systems undergoing a percolation transition is dramatically affected by their topological Berry phase

2\pi\rho

. For irrational

\rho

, we demonstrate that the low-energy excitations of diluted Josephson-junctions arrays, quantum antiferromagnets, and interacting bosons are spinless fermions with fractal spectrum. As a result, critical properties not captured by the usual Ginzburg-Landau-Wilson description of phase transitions emerge, such as complex critical exponents, log-periodic oscillations and dynamically broken scale-invariance.

{E}_{J}∕{k}_{B}

with the Josephson coupling strength

{E}_{J}

), the correlation length critical exponent $\ensuremath{\nu}=1.2$, and the dynamic critical exponent

z=2.0

in the strong disorder regime agree with the existing studies of the 2D gauge-glass model.